The mutual information between the input and output in (22) is calculated by the signal received by the first antenna of the \(m^{\prime } - th\)  receive antenna pair, i.e., \({y_{m^{\prime },1}}\) . Since the selection of the receive antenna only depends on the transmission antenna index, the mean of the mutual information corresponding to all receive antenna pairs is the average mutual information of OAM-SM millimeter wave communication systems considering all possible selections of transmission antennas. Moreover, the average mutual information in (22) is maximized when discrete inputs are uniformly distributed [1]}. In this paper discrete inputs, i.e., the transmission antenna index, the OAM state and the radiated symbol are governed by uniform distributions. Therefore, the average mutual information in (22) is maximized and then the DCMC capacity of OAM-SM millimeter wave communication systems is obtained. Based on (20) and (21), the PDF \(\mathcal {P}\left( {{y_{m^{\prime },1}},m,l,{x_p}} \right)\)  in (22) is derived by
\({\begin{array}{c}\mathcal {P}\left( {{y_{m^{\prime },1}},m,l,{x_p}} \right) = \mathcal {P}\left( {{y_{m^{\prime },1}}\left| {m,l,{x_p}} \right.} \right)\mathcal {P}\left( {m,l,{x_p}} \right) \hfill \\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \frac{1}{{MLP}}\mathcal {P}\left( {{y_{m^{\prime },1}}\left| {m,l,{x_p}} \right.} \right) \hfill \\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \frac{1}{{\pi \sigma _{\mathbf {w}}^2MLP}}\exp \left( { - \frac{{{{\left| {{y_{m^{\prime },1}} - \sqrt{\rho }h_{mm^{\prime },1}^l{x_p}} \right|}^2}}}{{\sigma _{\mathbf {w}}^2}}} \right) \hfill \\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathop = \limits ^{\left( a \right)} \frac{1}{{\pi \sigma _{\mathbf {w}}^2MLP}}\exp \left( { - \frac{{{{\left| {{w_{m^{\prime },1}}} \right|}^2}}}{{\sigma _{\mathbf {w}}^2}}} \right) \hfill \\\end{array}} ,\qquad \mathrm {(23)}\) 
